To find the difference \((3 - 2x + 2x^2) - (4x - 5 + 3x^2)\), we first distribute the negative sign across the second expression:
\[ (3 - 2x + 2x^2) - (4x - 5 + 3x^2) = 3 - 2x + 2x^2 - 4x + 5 - 3x^2 \]
Next, we combine like terms.
- The constant terms: \(3 + 5 = 8\).
- The \(x\) terms: \(-2x - 4x = -6x\).
- The \(x^2\) terms: \(2x^2 - 3x^2 = -1x^2\) (or simply \(-x^2\)).
Putting it all together, we get:
\[ 8 - 6x - x^2 \]
Thus, the final result for the difference is:
\[ -x^2 - 6x + 8 \]
If you would like to write it in standard form, it can be presented as:
\[ -x^2 - 6x + 8 = -1x^2 - 6x + 8 \]
Or simply:
\[ -x^2 - 6x + 8 \]
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